An inverse problem and a time-like Carleman estimate for parabolic integro-differential equations

2017/10/10 by Kawamoto, Atsushi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.03674

Abstract

In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of Hölder type for the inverse source problem in a cylindrical shaped domain. Our methodology is based on the Bukhgeim-Klibanov method by means of the Carleman estimate. Here we also derive the "time-like" Carleman estimate for parabolic integro-differential equations.

Related

• Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate
• Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates
• Inverse parabolic problems by Carleman estimates with data taken initial or final time moment of observation
• Conditional stability in determining source terms of semilinear parabolic partial differential equations
• Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate